Smoothing of likelihood ratio statistic for equiprobable multinomial goodness-of-fit

The likelihood ratio chi-square criterion for testing goodness-of-fit in k cell multinomials is known to overestimate significance for small and moderate sample sizes (see, e.g., Larntz (1978)). Therefore, the usual chi-square approximation to the upper tail of the likelihood ratio statistic G ², is not satisfactory. Several authors have derived adjustments (e.g., Williams (1976), Smith et al. (1981), Hosmane (1987b)), so that the asymptotic mean of G ² matches the mean of the asymptotic chi-square distribution in the hope that the distribution of G ² would improve. In this paper, a new adjustment to G ² is determined on the basis of the n ^-1-order term (n being the total number) of the Edgeworth expansion of the distribution of smoothed G ². Monte Carlo results indicate that the modified G ² outperforms the unadjusted G ².     

Studies on the effects of energy gap anisotropy in magnetically doped superconductors

The ultrasonic longitudinal sound wave attenuation coefficient and nuclear spin relaxation rate have been calculated for an anisotropic superconductor containing paramagnetic impurities with local states within the gap. The local states within the gap is shown to be anisotropic.     

Synthesis and characterization of Ru/Au,Pd/Au,Pd/2Au,Pt/2Au and Cu/2Au heterometallic complexes of cyclodiphosphazane cis-{(o-MeOC6H4O)P(μ-NBu)}2

Mononuclear complexes of cyclodiphosphazane with an uncoordinated phosphorus centre [RuCl₂(η⁶-cymene){l-κP}] (1a) (L = cis-{(o-MeOC₆H₄O)P(μ-N^tBu)}₂) and [PdCl₂(PEt₃){l-κP}] (1b) react with 1 equiv. of [AuCl(SMe₂)] to afford Ru^II/Au^I and Pd^II/Au^I heterodinuclear complexes [RuCl₂(η⁶-cymene){μ-l-κP,κP}AuCl] (2) and [PdCl₂(PEt₃){μ-l-κP,κP}AuCl] (3), respectively. Heterotrinuclear complexes [PdCl₂{μ-l-κP,κP}₂(AuCl)₂] (4), [PtCl₂{μ-l-κP,κP}₂(AuCl)₂] (5) and [CuI{μ-l-κP,κP}₂(AuCl)₂] (6) containing Pd^II/2Au^I, Pt^II/2Au^I and Cu^I/2Au^I metal centers have been synthesized from the reactions of trans-[PdCl₂{l-κP}₂] (1c), cis-[PtCl₂{l-κP}₂] (1d) and [CuI{{l-κP}₂] (1f) respectively, with 2 equiv. of [AuCl(SMe₂)]. Molecular structures of complexes 2, 3 and 4 were established by single crystal X-ray diffraction studies.     

Titanium tetrachloride mediated reductive ring opening of C-aryl pseudoglycals

A facile reductive ring opening of C-aryl pseudoglycals is reported for the first time. The combination of titanium tetrachloride (Lewis acid) and triethylsilane (reducing agent) at −78 °C in dichloromethane is a mild and efficient reagent system for this transformation. The reagent system was successfully tested on various C-aryl pseudoglycal substrates to yield the corresponding ring opened products containing two asymmetric hydroxyls and a cis-double bond.     

Novel octanuclear copper(I) metallomacrocycles and their transformation into hexanuclear 2-dimensional grids of copper(i) coordination polymers containing cyclodiphosphazanes, [(micro-NtBuP)2(NC4H8X)2] (X = NMe, O)

Novel octanuclear copper(I) macrocyclic complexes and hexanuclear 2-dimensional grid-like polymers containing [P(micro-NR)](2) scaffold in which the anionic moieties are trapped inside the cationic macrocyclic cavities are reported.     

Sterically Demanding Novel Triazole Based Tertiary Phosphines: Synthesis,Transition Metal Chemistry and Catalytic Applications

Sterically demanding 2,6-dibenzhydryl-4-methylphenyl and 1,2,3-triazole based tertiary phosphines, [Ar*{1,2,3-N₃C(Ph)C(PR₂)}] (R=Ph, 3 ; R=ⁱPr, 4 ) were obtained by the temperature-controlled lithiation of 1-(2,6-dibenzydryl-4-methyl)-5-iodo-4-phenyl-1H-1,2,3-triazole ( 2 ) followed by the reaction with R₂PCl (R=Ph, ⁱPr). Treatment of 3 with H₂O₂, elemental sulfur and selenium yielded chalcogenides [Ar*{1,2,3-N₃C(Ph)C(P(E)Ph₂)}] (E=O, 5 ; E=S, 6 ; E=Se, 7 ). The reaction of 3 with [Pd(COD)Cl₂] in 1 : 1 molar ratio, afforded dimeric complex [Pd(μ₂-Cl)Cl{Ar*{1,2,3-N₃C(Ph)C(PPh₂)}-κ¹-P}]₂ ( 8 ), whereas the reactions of 3 and 4 with [Pd(η³-C₃H₅)Cl]₂ in 2 : 1 molar ratios produced complexes [Pd(η³-C₃H₅)Cl{Ar*{1,2,3-N₃C(Ph)C(PR₂)}-κ¹-P}] (R=Ph, 9 ; R=ⁱPr, 10 ). Treatment of 3 with [Pd(OAc)₂] in 1 : 1 molar ratio afforded a rare trinuclear complex [{Pd₃(OAc)₄}{Ar*{1,2,3-N₃C(C₆H₄)C(PPh₂)}-κ²-C,P}₂] ( 11 ). Treatment of 3 and 4 with [AuCl(SMe₂)] resulted in [AuCl{Ar*{1,2,3-N₃C(Ph)C(PR₂)}-κ¹-P}] (R=Ph, 12 ; R=ⁱPr, 13 ). Bulky phosphine 4 was very effective in Suzuki-Miyaura coupling and amination reactions with very low catalyst loading. Molecular structures of 3 – 5 , and 8 – 13 were confirmed by single-crystal X-ray diffraction studies.     

Methylene insertion into the exocyclic P-N bonds of bis(amido)cyclodiphosphazane, cis-[Bu(H)NP(μ-BuN)]2

The 1:2 and 1:1 reactions of cis-[^tBu(H)NP(μ-^tBuN)]₂ (1) with paraformaldehyde afforded α-aminophosphonates, cis-[^tBu(H)NCH₂(O)P(μ-^tBuN)]₂ (2) and cis-[^tBu(H)NP(μ-^tBuN)₂P(O)CH₂N(H)^tBu] (3), respectively, through the insertion of a methylene moiety into the P-N bonds. The X-ray crystal structure of 2 reveals that the insertion reaction occurs selectively at the exocyclic P-N bonds of bis(amido)cyclodiphosphazane.     

Highly air-stable anionic mononuclear and neutral binuclear palladium(II) complexes for C-C and C-N bond-forming reactions

The short-bite aminobis(phosphonite), PhN{P(-OC10H6(mu-S)C10H6O-)}2 (2), containing a mesocyclic thioether backbone is synthesized by either treating PhN(PCl2)2 with 2 equiv of thiobis(2,2'-naphthol) or reacting chlorophosphite (-OC10H6(mu-S)C10H6O-)PCl (1) with aniline in the presence of a base. Treatment of 2 with an equimolar amount of Pd(COD)Cl2 in the presence of H2O affords a P-N-P-bridged and P,S-metalated binuclear complex, [PhN(P(-OC10H6(mu-S)C10H6O-)-kappaP)2Pd2Cl2{P(-OC10H6(mu-S)C10H6O-)(O)-kappaP,kappaS}2] (3), whereas the same reaction with 2 equiv of Pd(COD)Cl2 in the presence of H2O and Et3N produces the mononuclear anionic complex [{(-OC10H6(mu-S)C10H6O-)P(O)-kappaP,kappaS}PdCl2](Et3NH) (5). By contrast, reaction of 2 with 2 equiv of Pd(COD)Cl2 and H2O in the absence of Et3N gives the hydrogen phosphonate coordinated complex [{(-OC10H6(mu-S)C10H6O-)P(OH)}PdCl2] (4) which converts to the anionic complex in solution or in the presence of a base. Compound 2 on treatment with Pt(COD)X2 (X = Cl or I) afforded P-coordinated four-membered chelate complexes [PhN(P(-OC10H6(mu-S)C10H6O-)-kappaP)2PtX2] (6 X = Cl, 7 X = I). The crystal structures of compounds 2, 3, 5, and 7 are reported. Compound 3 is the first example of a crystallographically characterized binuclear palladium complex containing a bidentate bridging ligand and its hydrolyzed fragments forming metallacycles containing a palladium-phosphorus sigma bond. All palladium complexes proved to be very good catalysts for the Suzuki-Miyaura and Mizoroki-Heck cross-coupling and amination reactions with excellent turnover numbers (TON up to 1.46 x 105 in the case of the Suzuki-Miyaura reaction).     

Copper(I) complexes of bis(2-(diphenylphosphino)phenyl) ether: synthesis, reactivity, and theoretical calculations

The tricoordinated cationic Cu(I) complex [Cu(kappa2-P,P'-DPEphos)(kappa1-P-DPEphos)][BF4] (1) (DPEphos = bis(2-(diphenylphosphino)phenyl) ether) containing a dangling phosphorus center was synthesized from the reaction of [Cu(CH3CN)4][BF4] with DPEphos in a 1:2 molar ratio in dichloromethane. When complex 1 is treated with MnO2, elemental sulfur, or selenium, the uncoordinated phosphorus atom undergoes oxidation to form a P=E bond resulting in the formation of complexes of the type [Cu(kappa2-P,P'-DPEphos)(kappa2-P,E-DPEphos-E)][BF4] (2, E = O; 3, E = S; 4, E = Se) containing a Cu-E bond. The zigzag polymeric CuI complex [Cu(kappa2-P,P'-DPEphos)(micro-4,4'-bpy)]n[BF4]n (5) was prepared by the reaction of [Cu(CH3CN)4][BF4] with DPEphos and 4,4'-bipyridine in an equimolar ratio. The stereochemical influences of DPEphos on its coordination behavior are examined by density functional theory calculations.